The second-order nonlinear conductivity σ(2) describes the current generated in proportion to the square of the applied electric field and is equal to zero unless the medium breaks inversion symmetry. Recently, we reported a giant, anisotropic σ(2) at photon energy 1.5 eV in TaAs, a polar Weyl semimetal, that is larger than previously measured in any crystal. Subsequently, we measured the spectrum of σ(2)(ω) from 0.4 to 1.6 eV and found that the response at 1.5 eV is, in fact, the high-energy tail of a sharp resonance at 0.7 eV. Our discovery of a giant anisotropic σ(2)(ω) in TaAs raises the following questions: what is special about TaAs and/or polar metals that accounts for large resonant optical nonlinearity, and, is there a fundamental upper bound on σ(2)(ω) in such inversion breaking crystals? After describing the experimental findings, I will describe a simple model based on the band-geometric theory of nonlinear optical response that addresses these questions. The model is relevant to applications that attempt to use intrinsic inversion breaking to convert optical power to electrical current.

*We acknowledge support from the Quantum Materials Program at LBNL, funded by the US Department of Energy under Contract No. DE-AC02-05CH11231. J.O., L.W. and A.L. received additional support from Gordon and Betty Moore Foundation's EPiQS Initiative through Grant GBMF4537 to J.O. at UC Berkeley. J.A. rece

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.MAR.Y05.1